I am looking for a simple USB GPIO solution that supports interrupts to avoid needing additional threads/processes to constantly poll the device. Does the FT232H support any form of interrupts on any of the pins?

It does not. Additionally since you're asking in the CircuitPython and MicroPython forum, I'll add that CircuitPython does not currently support interrupts from user code so there won't be any API in Blinka to support it either.

The MCP2221 does appear to have interrupt support however you'd have to find a library and environment that supports the interrupt features.